Multiply: 7/16 x 2 2/7, reduced to lowest terms

The ratio 0.5:20=X:200 to proportion equation becomes

\(\frac{0.5}{20}=\frac{X}{200}\)

Cross-multiply to find the value of X

\(0.5\ast200=20X\)

\(100=20X\)

Divide both sides by 20 to find the value of X

\(\frac{100}{20}=\frac{20X}{20}\)

\(5=X\)

Thus, the value of X is 5.

A ratio of the form a:b=c:d converted to a proportion equation becomes\(\frac{a}{b}=\frac{c}{d}\)where\(a\ and\ d\neq0\)

Thus, 9:X=5:300 becomes

\(\frac{9}{X}=\frac{5}{300}\)

Cross-multiply to find the value of X

\(9\ast300=5X\)

\(2700=5X\)

Rearranging the above equation

\(5X=2700\)

Divide each side by 5

\(\frac{5X}{5}=\frac{2700}{5}\)

\(X=540\)

The value of X is 540.

Remaining fraction=\(1-\frac{1}{3}=\frac{3}{3}-\frac{1}{3}=\frac{2}{3}\)

Number of remaining books\(\frac{2}{3}\ast67982=\frac{135964}{3}\ books\)

Number of non-fiction books is 25% (100-75) of the remaining books

\(\frac{25}{100}\ast\frac{135964}{3}\ books=11330.333\ books\)

Thus, the number of non-fictional books is 11330.

First convert the mixed fraction into improper fraction as follows

\(2 2/7=\frac{\left(2\ast7\right)+2}{7}=\frac{14+2}{7}=\frac{16}{7}\)

Then, multiply the fractions

7/16 x 2 2/7=\(\frac{\mathbf{7}}{\mathbf{16}}*\frac{\mathbf{16}}{\mathbf{7}}=1\)

16 cancels with 16 while 7 cancels with 7 and the result becomes 1.